Using Letters to denote coordinate points and intervals On a graph with certain points denoted by letters, can you refer to intervals of the domain (let's say where the graph is increasing) using letters? For example, let's say $A (-1,-1)$ and $B (2,3)$ is an interval where the graph is increasing. Can I say, $(A,B)$ is the interval of increase?
 A: If I understand what you are saying, then what you want to express can simply be said by saying that $(-1,2)$ (the interval, not the point) is the interval of increase.
A: You better say, that in $[-1,2]$ the graph of the function is increasing. The letters $A$ and $B$ denote points on the graph of the function and not on the domain of the function. Knowing this, both following formulations sound correct to me:


*

*the graph of the function is increasing between points $A$ and $B$, or

*the graph of the function is increasing when the input variable (ok, a too formal term for $x$) is between $-1$ and $2$.

A: depends on what your instructor wants. if you can make (A,B) well defined, then it should be okay. personally, I would do it. 
A: I assume you mean that $A(-1,-1)$ and $B(2,3)$ are points on the graph of a function (call it $f$).
Technically one should say that the function is increasing on the interval $[x_A,x_B]\equiv[-1,2]$ between the domain values $x_A=-1$ and $x_B=2$ (this interval is the projection of the indicated portion of the graph down onto the $x$-axis).
The thing that is increasing is the associated value $y=f(x)$ as $x$ varies through that interval: $f(x)$ increases from $y_A=f(-1)=-1$ to $y_B=f(2)=3$.
The reason is that you have to be comparing real numbers, not points, to say that they are increasing. Points don't increase, because there is not a natural order for points. You can't say $B>A$, for example; but you can say $3>-1$. So you let one variable change ($x$), and observe the behavior of the other variable ($y$) to see if it is increasing, decreasing, etc. Since the relationship between $x$ and $y$ is $f$ (because $y=f(x)$), we then say (perhaps sloppily) that "$f$ is increasing on the domain interval $[-1,2]$".
